Video Texture Resolution in BGE
The answer is : "Play with the UV unwrapped mesh till it gets better".

Although I imported as plane and I thought this would be enough it isn't.

You need to move the vertices of the uv-unwrapped mesh and check what it produces. After some testing I brought it to levels that it is not pixelated. 

I would like though, to know what is the exact size in that unwrapped mesh to match the video perfectly. Comment if anyone knows.